Research Article · Research Article Theme: Challenges and Opportunities in Pediatric Drug Development Guest Editors: Bernd Meibohm, Jeffrey S. Barrett, and Gregory Knipp Physiologically

Research ArticleTheme: Challenges and Opportunities in Pediatric Drug DevelopmentGuest Editors: Bernd Meibohm, Jeffrey S. Barrett, and Gregory Knipp

Physiologically Based Pharmacokinetic Models in the Prediction of Oral DrugExposure Over the Entire Pediatric Age Range—Sotalol as a Model Drug

Feras Khalil1 and Stephanie Läer2,3

Received 31 July 2013; accepted 3 December 2013; published online 8 January 2014

Abstract. In recent years, the increased interest in pediatric research has enforced the role ofphysiologically based pharmacokinetic (PBPK) models in pediatric drug development. However, anexisting lack of published examples contributes to some uncertainties about the reliability of theirpredictions of oral drug exposure. Developing and validating pediatric PBPK models for oral drugapplication shall enrich our knowledge about their limitations and lead to a better use of the generateddata. This study was conducted to investigate how whole-body PBPK models describe the oralpharmacokinetics of sotalol over the entire pediatric age. Two leading software tools for whole-bodyPBPK modeling: Simcyp® (Simcyp Ltd, Sheffield, UK) and PK-SIM® (Bayer Technology ServicesGmbH, Leverkusen, Germany), were used. Each PBPK model was first validated in adults before scalingto children. Model input parameters were collected from the literature and clinical data for 80 childrenwere used to compare predicted and observed values. The results obtained by both models werecomparable and gave an adequate description of sotalol pharmacokinetics in adults and in almost allpediatric age groups. Only in neonates, the mean ratio(Obs/Pred) for any PK parameter exceeded a twofolderror range, 2.56 (95% confidence interval (CI), 2.10–3.49) and 2.15 (95% CI, 1.77–2.99) for area underthe plasma concentration-time curve from the first to the last concentration point and maximalconcentration (Cmax) using SIMCYP® and 2.37 (95% CI, 1.76–3.25) for time to reach Cmax using PK-SIM®. The two PBPK models evaluated in this study reflected properly the age-related pharmacokineticchanges and predicted adequately the oral sotalol exposure in children of different ages, except inneonates.

KEY WORDS: administration (oral); child; computer simulation; pharmacokinetics; sotalol.

INTRODUCTION

Physiologically based pharmacokinetic (PBPK) modelscan deliver valuable information during various stages of drugdevelopment and research (1–4). Their ability to incorporateinformation about maturation, growth, and age dependencyof anatomical and physiological processes facilitates their useto extrapolate drug pharmacokinetics from adults to childrenand to explore age-related changes (5,6). In recent years, theimplementation of PBPK models in pediatric drug develop-ment has become more attractive (7–11), encouraged by anincreased awareness of/and interest in pediatric research,especially after the new regulations on medicinal products forpediatric use in both the USA and the European Union (12,13).

Despite the marked potential of PBPK models, uncer-tainties still exist in the pediatric community about the accuracyof their predictions especially after oral drug administration inpediatric patients of different ages (11). The lack of sufficientpublished pediatric PBPK models evaluated adequately for theprediction of oral drug absorption and disposition is one mainreason. For the intravenous (IV) application, six pediatricwhole-body PBPK models evaluated with a total of 10 differentdrugs have already been reported (4,14–18). By contrast, thereis only, to date of writing, two publications with reportedpediatric PBPK model predictions evaluated for 6 drugs afteroral drug application (4,19), with only one of them evaluatedwith neonatal experimental data for the modeled drug (19). Inaddition, there are other reported pediatric PBPK models thatwere, however, either not evaluated with experimental data(20,21), or focused only on one aspect of the drug pharmaco-kinetics with no full concentration-time profiles or informationabout predicted drug absorption or exposure, e.g., to predictonly the clearance of the drugs (22,23). Given all of these facts,more examples of evaluated pediatric PBPK models for oraldrugs are still in demand.

In recognition of this unmet need, a PBPK model drugwith an already available large-scale clinical pharmacokinetic

1 Institute of Clinical Pharmacy and Pharmacotherapy, Heinrich-Heine University of Düsseldorf, Universitaetsstrasse1, Building.26.22. Room 02.21, 40225 Düsseldorf, Germany.

2 Institute of Clinical Pharmacy and Pharmacotherapy, Heinrich-Heine University of Düsseldorf, Universitaetsstrasse1, Building.26.22. Room 02.24, 40225 Düsseldorf, Germany.

3 To whom correspondence should be addressed. (e-mail:[email protected])

The AAPS Journal, Vol. 16, No. 2, March 2014 (# 2014)DOI: 10.1208/s12248-013-9555-6

1550-7416/14/0 00-0226/0 # 2014 The Author(s). This article is published with open access at Springerlink.com 2262

data set that covers all pediatric age groups is preferable.Sotalol, an antiarrhythmic drug used in the treatment ofsupraventricular tachycardia, orally given with >90% bioavail-ability and almost completely renally eliminated, has been verywell studied in both adults and children and fulfills thisrequirement (24–37). The rich pediatric data of sotalol facilitatea good assessment of the model predictability from adolescentsdown to neonates, and provide individual full concentration-time profiles with information on drug absorption. Conversely,the rich adult data after both IV and oral administration willenable the validation of themodel first in adults before scaling itto children, thus forming a solid basis for age extrapolation.Finally, because commercial PBPKmodeling packages are oftenused nowadays by researchers as a basis for their models, andbecause no single source for the integrated data does exist, thechoice to use two commonly used modeling software tools formodel development has been undertaken to minimize bias bysoftware and to examine to what extent the use of differentmodeling software can influence the obtained results.

This study was made to investigate how whole-bodyPBPK models, developed using two dedicated PBPK model-ing tools, describe the oral pharmacokinetics of sotalol fromadults to neonates. A secondary goal was to observe anydifferences in the performance of these two models across thepediatric age range.

MATERIALS AND METHODS

PBPK Modeling Software and Model Parameterization

To develop a whole-body PBPK model of sotalol, twospecialized modeling software tools were used separately:software 1 was Simcyp® simulator v.12.1 (Simcyp Ltd,Sheffield, UK) for adults and pediatrics (38), and software 2was PK-SIM® v.4.2.2 (Bayer Technology Services GmbH,Leverkusen, Germany) with its integrated clearance scalingmodule (39). In brief, these tools provide a general PBPKmodel structure to describe drug absorption and dispositionin the body and incorporate a large data set of anatomical andphysiological parameters with their age dependencies, aspermitted by the current scientific knowledge. The detailedstructure and methodology of these PBPK models are alreadypublished elsewhere (40,41).

However, to complete the model parameterization, therequired physicochemical properties of sotalol, along with otherdrug-dependent parameters, were collected from a comprehen-sive literature search. Both models used the same values formolecular weight, lipophilicity (octanol–water partition coeffi-cient (logP) value), acid dissociation constant (pKa), fractionunbound (fu), and clearance (CL), as listed in Table I(24,25,31,43,47,60), which summarizes the final model inputparameters. The total clearance of sotalol was set to be0.1125 L h−1 kg−1 assigned completely as a renal clearance,which is consistent, in its value and the route of elimination, withthe literature (24,25,31). The partition coefficients in the tissueswere calculated with both software using Rodgers andRowland’s distribution model (42). The input values assignedto the blood-to-plasma concentration (B/P) ratio differedbetween software 1 and 2 (1.02 vs. 0.86), as these values gavethe best visual fit during the IV model development (seeModeling Strategy and Simulation Conditions); however, the

models predicted similar Vss values, 1.3 and 1.22 L/kg,respectively, in an average adult male individual weighing70 kg, which are in good agreement with the reportedliterature values (24,31,43,44). Drug absorption was predictedby the advanced dissolution, absorption, and metabolism(ADAM) model in Simcyp (45), and by a built-in absorptionmodel in PK-SIM (46), with various input measures offered bythe two software to account for the drug intestinal permeability.Sotalol is known to be a biopharmaceutics classification system(BCS) Class I drug with high solubility and high permeabilityprofile; however, sotalol in vitro measured apparentpermeability coefficient (Papp) is very low and does notcorrelate with the high values of absorbed dose fraction(>90%) obtained from pharmacokinetic studies in humans(47,48). Therefore, the value of the intestinal permeabilitymeasure for each model was adjusted separately in order togive the same absorbed fraction and a bioavailability of 90% inadult. Finally, the default mean values used in both models forgastric emptying time (GET) and small intestinal transit time(SITT) were 0.5 and 4 h, respectively.

Pharmacokinetic/Clinical Data

In Adults. MEDLINE database was screened for phar-macokinetic studies of sotalol in healthy adults with knownage, gender, height or weight, clear dosing information, andavailable plasma concentration-time profiles. As a result, atotal of 27 data sets originating from 11 clinical trialspublished by 8 different scientific groups (between 1976 and2010) in 5 countries (26–36) were used in model developmentand evaluation (Table II) (26–36). Each experimental data setrepresents a mean observed concentration-time profile in anaverage of five to six healthy volunteers who received eitherIV or oral doses of sotalol-HCl. These data were eitherprovided by the author (35,36) or scanned from the publica-tions’ figures (26–34).

In Children. Eighty pediatric patients of different agegroups with known age, gender, height, weight, dosinginformation, and measured plasma profiles were used. Themajority of these data are already published (37). Thesepatients, ranging from age 11 days to 17.7 years (average,3.51 years, including 13 premature infants) received variousdoses of sotalol (1.0–9.9 mg kg−1 day−1) for the treatment ofsupraventricular tachycardia. The demographics of thesechildren are presented in Fig. 1. This pediatric data set wasclassified using a system similar to the WHO classification,however, using six different age groups: (a) neonates, 0–28 days (n=14); (b) infants, 1–11 months (n=33); (c) toddlers,12–23 months (n=6); (d) Preschool-aged, 2–5 years (n=10);(e) school-aged, 6–11 years (n=13); and (f) adolescents, 12–18 years (n=4). This classification was used for presentingresults in children.

Modeling Strategy and Simulation Conditions

The adopted modeling strategy is shown in Fig. 2. Anadult model was first developed for the IV application, as thisallows for the kinetics of drug disposition to be simulated in

227PBPK Models to Predict Pediatric Oral Drug Exposure

the absence of the complexities of the absorption process.Thus, the best set of input parameters, the suitable distribu-tion model, and the most appropriate clearance that collec-tively gave the best visual description of the observed dataused at this stage, were assigned. For the oral application,parameters values from the previous step were kept plus thevalues of additional parameters that control and influencedrug absorption, such as intestinal permeability, GET, andSITT. In the previously mentioned steps (i.e., model build-ing), only one fifth (n=5) of the collected adult data set wasused, whereas the remaining data (n=22) were used later fora subsequent model verification. The adult model was slightlyrefined (logP and CL inputs) before the end model evalua-tion. The final adult model was then scaled down to children,taking into consideration the age dependencies of anatomicaland physiological processes/parameters and the ontogeny ofclearance pathways, which are already integrated into the

modeling software, to predict pediatric sotalol exposure (seealso, Clearance Scaling).

The comparison of model results with observed data wasbased on simulations of virtual populations, where the mainresults of these simulations are concentration-time profiles. Inadults, each virtual population consisted of 100 virtualsubjects having the same age range, race, gender composition,and dosing as their respective real population. The resultingmean plasma concentrations were then compared with themean observed concentrations for model evaluation.Population simulations performed with a higher number ofvirtual subjects (n=1,000) did not produce any significantdifference from the previous ones (using 100 replicates), anddid not influence any differences seen between the results ofboth models. In children, a similar approach was used byperforming a population simulation of 100 virtual childreneach with the same age, race, gender, and dosing information

Table I. Input Parameters for Sotalol PBPK Models Using Both Modeling Software

Parameter Software 1a value Software 2b value Reference value Reference

Molecular weight (g/mol) 272.36 272.36 272.36 PubChemLogP(o/w) 0.37 0.37 0.2, 0.37 PubChem, (47)Ionization constant pKa1=8.28 pKa1=8.28 pKa1=8.28 (60)

pKa2=9.72 pKa2=9.72 pKa2=9.72fu 1 1 1 (24,25,43)Blood/plasma ratio 1.02 0.86 1.07 (60)CLIV, total 7.875 L/h 0.1125 L h−1 kg−1 0.09–3.2 L h−1 kg−1 (31,43,44)Fraction of renal clearance 100% 100% 90–100% (24,25)Permeability measure (cm/s)c 2.01×10−4c 12.6×10−6c – –

LogP octanol–water partition coefficient, fu fraction unbound, CLIV, total total intravenous clearance, pKa acid dissociation constant, pKa1 foracidic function, pKa2 for basic functiona Simcyp®b PK-SIM®cHuman jejunum permeability (Peff, man) as permeability measure in software 1; in vitro intestinal permeability (Papp) as permeabilitymeasure in software 2. Both measures were manually adjusted to give the same value of fraction absorbed (fa) and a bioavailability of 90%

Table II. Population Characteristics and Dosing Information of the Pharmacokinetic Studies Used in the Development and Validation of theSotalol Adult PBPK Model

Applied dose

No. of data setsa Ethnicity Females (%) Age range (years) References(mg) (mg/kg)

Intravenous sotalol 20 – 1 Caucasian 50 24–53 (26)35b 0.5 2 Caucasian 50 18–38 (27)70b 1 1 Asian 0 22–43 (28)75 – 1 Caucasian 60 19–45 (29)105b 1.5 4 Caucasian/Asian 18 18–43 (27,28,30)140b 2 2 Caucasian 0 21–32 (30,31)210b 3 2 Caucasian 50 18–38 (27)

Oral sotalol 40 – 1 Asian 0 22–45 (32)50 – 1 Asian 0 22–43 (28)80 – 2 Caucasian 60 19–45 (29,32)100 – 2 Caucasian/Asian 0 22–43 (31)160 – 5 Caucasian/Asian 16 22–56 (26,32,33,35,36)200 – 1 Asian 0 22–43 (28)300 – 1 Asian 0 22–43 (28)320 – 1 Caucasian 10 28–56 (34)

aEach data set represents a mean observed concentration time profile of an average of five to six healthy adult volunteersbTotal dose in milligrams was calculated from the reported milligrams per kilogram dose using a reference adult weight value of 70 kg

228 Khalil and Läer

of a real child; however, the resulting median plasmaconcentrations were used along with the individual observedconcentrations in the model evaluation. For all previoussimulations, variability ranges for CL, GET, and SITT wereassigned to account for the interindividual variability. Thesevalues were either set by the software, as in software 1—CL:mean value±30% CV; GET: mean value±38% CV; SITT:Weibull distribution around the mean value with α=2.92 andβ=4.04; or were assigned manually based on a comprehensiveliterature search as in software 2: lognormal distribution withgeometric standard deviation of 1.3 for CL, GET: uniformdistribution of 0.2–1.9 h in adults (49,50) and 0.2–2.1 h inchildren (51–54), and SITT: normal distribution with a meanvalue of 4±1 h in both (49,55).

Clearance Scaling

The modeling tools used here employ a physiology-basedscaling of adult clearance to children. In short, data sets ofexperimentally obtained clearances of various substances, forwhich elimination were primarily due to one process, werepreviously collected and used to develop and validate

ontogeny patterns accounting for the maturation of variouselimination pathways over the pediatric age, including renalelimination (22,23). These ontogeny profiles are incorporatedin the used modeling tools, and employed along age-specificdifferences in bodyweight, eliminating organs weight andblood flow, and protein binding in order to scale adultclearance value (model input) to children of different age.This physiology-based scaling of clearance was shown toaccurately predict clearance in children from birth toadolescence (22,23) and was found superior to that ofallometric scaling.

Evaluation of Model Performance

Visual predictive checks for superimposed predicted andobserved plasma concentration-time profiles, and goodness offit plots were used for the graphical analysis of model results.Moreover, the area under the plasma concentration-timecurve from the first to the last concentration point (AUClast),the maximal concentration (Cmax) with the time to reach it(tmax), and the elimination-rate constant (ke) were calculatedvia a noncompartmental analysis for each observed profile

Fig. 1. The height and/or weight (dots) of each of the 80 children (boys, n=54 (right); girls, n=26 (left)); the observedpopulation originally exposed to sotalol. In addition, lines show pediatric age- and gender-specific percentiles (3rd, 10th,50th, 90th, and 97th), which represent the normal values of a German representative population (61). Insets show thedemographics of the segment from birth to the end of the first year to highlight the values of newborns and infants


and its corresponding predicted value from each model.AUClast was calculated via the trapezoidal method, ke as theslope of the last three concentrations on a natural logarithmicscale (in children: only for plasma profiles measured over atleast 10 h, n=66/80), whereas Cmax and tmax were manuallydetermined as in definition. An observed/predicted ratio(ratioObs/Pred) was then calculated and the final results werereported as mean ratios(Obs/Pred) with a nonparametric 95%confidence interval (CI) derived from 10,000 bootstraprepetitions. A twofold error range from the observed valuesfor model predictions was set as a reference. Such a range iscommonly reported by other researchers and is consideredappropriate for a predictive model (14,16,19). Finally, per-centage error (PE) and absolute percentage error (APE)were calculated for every concentration point in each drugadministration in adults and children as follows:

PE ¼ CPRED−COBSð ÞCOBS

� 100% ð1Þ

APE ¼ CPRED−COBSj jCOBS

� 100% ð2Þ

To numerically describe the model accuracy and preci-sion, the median percentage error (MDPE) and medianabsolute percentage error (MDAPE; with a nonparametric

95% CI derived from 10,000 bootstrap repetitions) werereported, respectively, as suggested in Sheiner and Beal (56).All of the previously mentioned calculations were done usingMATLAB 2012a (57).

RESULTS

Simulation Results in Adults

A comparison between mean simulated and mean ob-served plasma concentration-time profiles for four representa-tive data sets in adults is shown in Fig. 3 (26,28,32,35). In general,the two presented models were able to accurately describesotalol exposure after IVand oral application over a total doserange of 20 to 320 mg (0.2–4.5 mg/kg BW) and for bothCaucasians and Asians. The resulted AUClast ratios(Obs/Pred)

were within 0.8–1.25 in 100% (27/27) and in 92.6% (25/27) ofthe observed values using software 1 and 2, respectively, andwith all predictions contained within the range 0.5–2.Moreover, the adult model did not show any difference inthe predictability of sotalol exposure after IV or oralapplication. The mean AUClast ratio(Obs/Pred) for all simulat-ed data sets using software 1 was 0.997 and 0.94 after IV andoral applications, respectively. These results were similarusing software 2 as the mean AUClast ratio(Obs/Pred) was 0.94for the IV and 0.987 for the oral application. Figure 4 showsthe predicted vs. observed plots for plasma concentrations,AUClast, Cmax, tmax, and ke.

Fig. 2. Schematic workflow of the developed PBPK models


The calculated numerical metrics indicate good accuracyby both models. Software 1 showed no bias with a MDPE

value (95th bootstrap CI) of 1.36% (−1.37 to 3.17), incomparison to a slight bias of 3.17% (1.63–5.23) in the model

Fig. 3. Comparison of predicted (lines; mean, 5–95th percentiles, min/max) and mean observed (dots; ±SD) concentrationsof IV and oral sotalol after various dosing in both Caucasians (a, b) and Asians (c, d). Simulations were performed usingsoftware 1 (SIMCYP®, left column, filled circles) and 2 (PK-SIM®, right column, empty circles). Observed data are obtainedfrom Refs. (26,28,32,35)


Fig. 4. Goodness of fit plots for simulations of adult data by both sotalol PBPK models. a Predicted vs. observedconcentrations plot, b–e predicted vs. observed AUClast, Cmax, tmax, and ke plots. Results are obtained by using software 1(SIMCYP®, left column, filled circles) and software 2 (PK-SIM®, right column, empty circles). Line, line of unity; dashedlines, twofold error range; MDPE median percentage error (95% CI), MDAPE median absolute percentage error (95% CI)


generated using software 2, which is, however, minimal and hasno clinical relevancy. Finally, both models showed similarprecision (deviation less than 10%) as the MDAPE for allpredicted concentration points was 9.91% (8.79–10.96) and9.76% (8.56–10.85) using software 1 and 2, respectively (Fig. 4).

Simulation Results in Pediatrics

Using both modeling software applications, the extrapo-lated model corresponding to the pediatric populationshowed acceptable correlated predictions to in vivo data inadolescents down to infants, with a pronounced deviation inneonates. A comparison between median simulated andobserved plasma profiles for six representative pediatricpatients of each age group is shown in Fig. 5 (37).

Only in neonates were the both models unable topredict a mean ratio(Obs/Pred) of all four PK parameterswithin the predefined twofold error range (Fig. 6). Usingsoftware 1, the mean ratios(Obs/Pred) were 2.56 (95% CI, 2.10–3.49) and 2.15 (95% CI, 1.77–2.99) for AUClast and Cmax,respectively. Using software 2, the mean ratio(Obs/Pred) of tmax

was 2.37 (95% CI, 1.76–3.25). The elimination-rate constantwas reasonably predicted by both models as indicated by amean ratio of 0.55 and 0.81 for the software 1 and the 2model, respectively.

In all remaining age groups, the mean ratios(Obs/Pred)

for the chosen PK parameters were within a twofold errorrange irrespective of the model used, which indicates agood predictive performance and a proper description ofthe age-related pharmacokinetic changes of sotalol. The95% CI of the mean ratios for all PK parameters wascontained within the range of 0.5 to 2, except for tmax insome age groups (Fig. 6).

Furthermore, both models showed a general tendencyto underestimate sotalol concentrations as seen with thenegative MDPE values in almost all age groups and thelower accuracy and precision values when compared withthe adult model (see Fig. 7). The least accuracy inpredicting individual concentration points was seen inneonates for software 1 (MDPE=−54.8%) and in infantsfor software 2 (MDPE=29.2%), whereas for both modelsthe highest accuracy was seen in adolescents. On theother hand, the pediatric model imprecision was less than40% in all groups except in neonates using software 1(MDAPE=54.8%) and in infants using software 2(MDAPE=43.6%), with the best model precision seen inadolescents using both software (MDAPE=15.7%, 15.6%for software 1 and 2, respectively).

DISCUSSION

Whole-body PBPK models for sotalol, an orally givendrug, were developed using two specialized modeling soft-ware tools. The presented models were able to successfullydescribe sotalol pharmacokinetics in adults and over a widerange of the pediatric age, except in neonates. The resultsobtained by both models were comparable and showeddifferences only in children under 1 year of age.

Following the methodological approach, PBPKmodels of sotalol were first developed and evaluated inadults. Both models were able to accurately and reliably

predict sotalol exposure after a wide range of IV and oraldosing (Figs. 3 and 4), which indicate that they adequatelycaptured the major processes driving sotalol pharmacoki-netics. The initial development and validation of themodel in adults present a modeling strategy that forms asolid basis for age extrapolation to increase the accuracyof the pediatric model predictions. Such a strategy iscommon in the development of pediatric models and isalready used by other researchers (16,17,19).

In adolescents down to infants, the pediatric modelsseemed to properly reflect the age-related changes in sotalolpharmacokinetics, as indicated by the adequate description ofthe experimental plasma profiles, which was further supportedby the numerical metrics and a good prediction of AUCtlast,Cmax, tmax, and ke indicated by a mean ratio(Obs/Pred) within atwofold error range (Figs. 5, 6, and 7). It was only for tmax,where the calculated 95%CI exceeded the twofold error rangein some age groups; however, this could be explained, exceptfor infants, by the relatively low number of included children.Comparing our results with the other available pediatric modelfor the oral application, Parrot et al. reported in a model for theoral oseltamivir and its metabolite a predicted AUC in infantsthat was within a twofold range of the observed value (19),which resembles our finding using both software for the sameage group.

In neonates, no model was able to predict a meanratio(Obs/Pred) for all reported PK parameters (AUClast, Cmax,tmax, and ke) within the predefined twofold error range, and,therefore, the results were judged as inadequate (Fig. 6). Thenoticed deviation was seen for parameters reflecting theextent and rate of drug absorption (AUClast, Cmax, or tmax)rather than drug disposition (ke). In the previously mentionedmodel by Parrot et al., a difference of more than twofold uponAUC prediction of oseltamivir and its metabolite in neonateswas obtained, which is similar to our findings (19). A meanratio(Obs/Pred) higher than two for any PK parameter—as inour results—implies that the model predicts a value that is, onaverage, less than half of the experimentally observed one.Nevertheless, the clinical relevancy of such results should beeventually judged taking additionally into consideration theintended use of the generated data, and the allowable errorby the drug (e.g., low for drugs with narrow therapeuticwindow). For example, this deviation seen in neonates wouldbe of more clinical relevancy if the model is intended to beused to make dose recommendations than to suggestsampling times. In the former case, any recommendations inneonates based on such low predicted AUC, in comparison tothe observed, could lead to recommending higher therapeuticdoses than necessary with potential toxicity (e.g., torsades depointes with sotalol) as a clinical consequence.

Both of the presented models performed similarly inadults and in almost all pediatric age groups with the onlydiscrepancy seen in children less than 1 year of age. First,whereas the software 1 model tended to under-predictplasma concentrations in all age groups, including infantsand neonates (negative MDPE), the software 2 modelunder-predicted plasma concentrations only in childrenover 1 year of age. Finally, in neonates, the software 1model was unable to accurately predict the extent of drugabsorption as indicated by a mean ratio(Obs/Pred) exceeding2 for AUClast and Cmax, whereas the software 2 model did


not adequately predict the rate of drug absorption (tmax)in the same age group.

We suggest that the inaccuracy of the predictions seen inneonates is attributed to the absorption rather than elimination or

distribution process. This is because the major factors thatinfluence sotalol disposition (e.g., maturation of the renalfunction, the age-related differences in body composition, tissuevolumes, and blood flows) are well characterized over the entire

Fig. 5. Comparison of predicted (lines; median, 5–95th percentiles) vs. individual observed (symbols) plasma concentrationsin six representative pediatric patients from adolescents (a) to neonates (f), after various dosing of oral sotalol. Predictionswere made using software 1 (Simcyp®, left, filled circles) and 2 (PK-SIM®, right, empty circles). Observed data are takenfrom Refs. (37)


pediatric age range and are successfully implemented in the usedmodeling tools, which should make the scaled information (e.g.,clearance) a good estimate. In this exercise, both models wereable to acceptably predict the elimination-rate constant in allpediatric age groups (Fig. 6). However, the marginally acceptedlow mean ratio(Obs/Pred) for ke in neonates, using software 1,indicate relatively high predicted values that are most probablyattributed to high predicted clearance in this age group. As aresult, the potential influence of any inaccuracy in clearancescaling on the obtained results in neonates should not becompletely excluded.

By contrast, the absorption process is more complex andinvolves many factors apart from the pharmaceutical formu-lation of the drug. The first set of them are anatomical andphysiological such as gastrointestinal organs volume andblood flow, radius, length and effective surface area, pH,GET, SITT, metabolizing enzymes, transporters, and fluidsecretion. Influenced, in part, by difficulties in obtaining age-specific information in the literature, an age-specific value isnot incorporated for all of these factors in the pediatricabsorption models integrated within the used modeling tools,which makes them an aspect to improve (Table III). Forinstance, the ADAM model used by software 1 to predict theoral drug absorption is under further improvement to fill suchgaps with age-specific values, e.g., for metabolizing enzymes,transporter, pH profile, and volume of secreted fluids. Assotalol is not metabolized, not actively transported through-out the gastrointestinal tract, and highly soluble, an age-related change in the pH profile could be the sole possiblefactor from this list to influence its extent of absorption.

The second set of parameters is drug dependent such assolubility, pKa, volume/size of the molecule and its intestinalpermeability. Concerning the latter, Yang et al. suggested

paracellular transport to play a major role in sotalolpermeability (47). Dahan et al. stated that, in adults, sotalolshows a unique permeability pattern as a combination of abasic moiety, with pKa and logP values within a critical range,and that sotalol permeability in the distal small intestine ishigh and compensates for its low permeability in the proximalsegments (58), which explains the low in vitro measuredjejunal permeability of sotalol, the BCS class I drug. Inrecognition of this information, the predictions of software 1model in neonates would have been improved, if a higherpermeability of sotalol is assumed and incorporated into themodel, as it has already been reported that paracellulartransport is higher in neonates than in adults because of widertight junctions (59). Conversely, the findings of Dahan et al.highlight the role of higher pH values in sotalol absorp-tion, and points out a rationale to incorporate differentvalues of permeability throughout the intestinal segments,which could improve software 2 model predictions.Running simulation scenarios by the presented PBPKpediatric models would clarify, reject, or confirm theseassumptions and would help in detecting the mostinfluential factor on sotalol absorption.

Limitations

The two presented models were not completely identical intheir input parameters (Table I); however, the different inputvalues of B/P ratio and intestinal permeability measures resultedeventually in similar Vss and bioavailability values and, thus, arenot likely to be responsible for any major finding. Second,although the work presented here would contribute to a betterunderstanding, and thus to a more correct use of the PBPKmodel-generated data in the pediatric population, sotalol is a

Fig. 6. Comparison between the observed and predicted values of a the area under the plasma concentration-time curve (AUClast), b maximumconcentration (Cmax), c time of the maximum concentration (tmax), and d the elimination-rate constant (ke) in adults oral studies and inchildren. Results are presented as mean ratios in each age group (symbols—circles for software 1 results, squares for software 2 results) with a95% confidence interval (horizontal lines)


drug with a relatively simple pharmacokinetic profile, i.e.,renally excreted, not metabolized, unbound to plasmaproteins, and is not known to be actively transported(24,25); therefore, the used software tools may notnecessarily do as well with predictions for drugs with

more complex pharmacokinetics. In addition to that,sotalol is a BCS class I drug with a high solubility and ahigh permeability profile, which means that this exercisewill give no information on the accuracy of the drugabsorption in the lower intestinal segments and its age

Fig. 7. Median predicted vs. individual observed concentration plots for 80 pediatric patients stratified in 6 pediatric agegroups from a adolescents to f neonates. Results are obtained by using software 1 (SIMCYP®, left column, filled circles) and2 (PK-SIM®, right column, empty circles). Line, line of unity; dashed lines, twofold error range; MDPE median percentageerror (95% CI), MDAPE median absolute percentage error (95% CI)


dependence. As a result, further examples with drugs thatpossess different pharmacokinetic profiles (e.g., hepaticelimination with first-pass effect or with involvement oftransporters) and physicochemical properties (e.g., ofdifferent BCS grouping) are still needed.

Implications and Generalizations

This work was not designed to investigate new insightson the pharmacokinetics of sotalol, as they are alreadyextensively studied in both adults and children (24–37).However, the current work is planned to support a futurepediatric clinical trial, which will aim to develop a safe IVdosing regimen as a substitution of oral sotalol in childrenwith supraventricular tachycardia by providing the necessarysampling times for an optimal pharmacokinetic analysis.Additionally, such validated models could play a role insupporting clinical decision making in individual patients, forexample, with reduced renal function.

The obtained results in infants through adolescentsindicate a good model predictability and, thus, substantiatethe use of PBPK models to generate data a priori for this agegroup, saving time, effort, and resources. This could beprobably generalized to other orally given drugs that sharea similar pharmacokinetic behavior as sotalol. Alternatively,the lower model predictability of sotalol pharmacokineticsseen in neonates indicates the need for a more cautious use ofmodel-generated data in this age group, acknowledging thatthe final judgment depends on the purpose of the model andthe properties of the modeled drug.

CONCLUSIONS

In summary, the PBPK models presented in this articlehave shown good predictability of observed data in adults andin almost all pediatric age groups, except in neonates where alower predictive performance was seen, which indicates amore cautious use of model-generated data in this age group.These results encourage the use of PBPK models, especiallywhen adult data are available, to predict oral drug exposurein a wide range of pediatric age, which can aid in supportingpediatric clinical trials, and, potentially, the clinical decisionmaking for individual children.

ACKNOWLEDGMENTS

The authors would like to thank Bayer technologyservices (PK-SIM®) and Certara (Simcyp®) for providingacademic licenses to use the software packages.

Open Access This article is distributed under the terms of theCreative Commons Attribution License which permits anyuse, distribution, and reproduction in any medium, providedthe original author(s) and the source are credited.

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Table III. List of the Anatomical, Physiological, and Drug-Specific Parameters that Are Involved in the Drug Absorption with the Availabilityof Corresponding Age-Specific Values, as Default, in the Used Pediatric Absorption Models

Software 1 Software 2

Anatomical and physiological parametersGIT organs volumes Scaled with age-specific data Scaled with age-specific dataGIT organs blood flows Scaled with age-specific data Scaled with age-specific dataRadius of the intestinal segments Scaled with age-specific data Scaled with age-specific dataLength of the intestinal segments Scaled with age-specific data Scaled with age-specific dataEffective surface area of intestinal segments Scaled with age-specific data Scaled with age-specific dataGastric pH Not scaled (adult values)a, b Not scaled (adult values)a

Intestinal pH Not scaled (adult values)a Not scaled (adult values)a

Gastric emptying time Not scaled (adult values)a Not scaled (adult values)a

Small intestinal transit time Not scaled (adult values)a Not scaled (adult values)a

Intestinal enzyme ontogeny Scaled for CYP3A4 and UGT Scaled for CYP3A4 and UGTIntestinal enzyme abundance Not scaled (adult values)c Not scaled (adult values)c

Intestinal transporter ontogeny Not scaled (adult values)c Not scaled (adult values)c

Intestinal transporter abundance Not scaled (adult values)c Not scaled (adult values)c

Fluid secretion volume Not scaled yetb Volumes are scaled according to lengthand radius of intestinal segments

Drug-specific parametersMolecular weight of the molecule Unchanged UnchangedpKa value Unchanged UnchangedLipophilicity Unchanged UnchangedSolubility Unchanged UnchangedPermeability coefficient in the gut wall Unchanged Unchanged

This list does not include factors related to the pharmaceutical formulationaValues and variability ranges could be manually assigned. In software 2, various distribution types of the variability could be assigned duringthe simulations of virtual populationsbTo be incorporated in the upcoming versionscNo sufficient literature of specific pediatric data


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